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APPLICATION OF THYRISTOR-CONTROLLED SERIES REACTOR FOR 
FAULT CURRENT LIMITATION AND POWER SYSTEM STABILITY 

ENHANCEMENT 

by 

Bu II Kang 

Bachelor of Science, Chonnam National University, 1994 



A thesis submitted to the 

Faculty of the Graduate School of the 

University of Colorado in partial fulfillment 

of the requirements for the degree of 

Master of Science 

Electrical Engineering 

2013 



This thesis for the Master of Science degree by 

Bu II Kang 

has been approved for the 

Electrical Engineering Program 

by 



Jae-Do Park, Chair 

Fernando Mancilla-David 

Yiming Deng 



April 16, 2013 



11 



Kang, Bu II (M.S., Electrical Engineering) 

Application of Thyristor-Controlled Series Reactor for Fault Current Limitation and 
Power System Stability Enhancement 

Thesis directed by Assistant Professor Jae-Do Park. 



ABSTRACT 

Various types of Fault Current Limiters (FCLs) have been proposed and proven 
that they offer many advantages with respect to transmission losses, voltage quality, and 
power system stability. However, those including the Solid-State Fault Current Limiters 
(SSFCL), the most advanced type of FCL, have been mainly focusing on the FCL system 
itself such as optimization of components, improving the efficiency and reducing the cost. 
Conventional ways such as splitting buses, replacing the switchgear, and installing 
permanently-inserted series reactor are still used to avoid fault current problems, which 
impairs overall power system reliability. In this thesis, a Thyristor-Controlled Series 
Reactor (TCSR) is presented to limit the fault current and enhance the power system 
stability simultaneously. The influence of TCSR is analyzed from the perspective of 
voltage security enhancement and the feasibility of real power system application is 
assessed. The benefits of the TCSR are demonstrated with bulk power system simulation 
results from the voltage security and angle stability stand point. 

The form and content of this abstract are approved. I recommend its publication. 

Approved: Jae-Do Park 



in 



DEDICATION 

I dedicate this work to Eungjeong, my lovely wife, who has always 
believed and supported me by my side. 



IV 



ACKNOWLEDGMENTS 

This thesis would not have been possible without the support of my company, 
Korea Power Exchange (KPX). 



TABLE OF CONTENTS 

CHAPTER 

I. INTRODUCTION 1 

Introduction 1 

II. FAULT CURRENT LIMITERS 3 

Fault Current Limitation by a Series Reactor 3 

Bypass Switch 4 

Tuned LC Circuit Shunted by a Metal Oxide Varistor (MOV) 5 

Series Compensator 6 

Power Electronic Switches 11 

III. POWER SYSTEM STABILITY 13 

Thyristor Controlled Series Compensator (TCSC) 17 

Short Circuit Current Limiter (SCCL) 20 

IV. D-Q TRANSFORMATION 22 

V. PROPOSED APPROACH 29 

Voltage Stabilizing Fault Current Limiter 29 

Plant Model and Compensator Design 32 

VI. COMPUTER SIMULATIONS 37 

Duty Control to Increase Output Voltage 37 

Effects of TCSR on Different Fault Locations 40 

Effects of TCSR on Bulk Power System Voltage Stability 44 

Effects of TCSR on Bulk Power System Angle Stability 46 

VII. CONCLUSION 51 



VI 



LIST OF TABLES 

Table 

VI. 1 Simulation parameters 38 

VI.2 Comparison results of the voltage and the fault current 45 

VI. 3 Fault current of the adjacent buses with respect to 4400 bus fault 48 

VI.4 Fault current of critical buses(kA) 48 

VI.5 Case summary(MW) 48 

VI.6 Critical Clearing Time(msec) 48 



vn 



LIST OF FIGURES 
Figure 

II. 1 Fault current limiter application: it protects the entire bus or individual circuit 4 

11.2 Relationship between system voltage drop, reactor short-circuit voltage and power 
factor 5 

11.3 Fault current limiter with tuned impedance 6 

11.4 Fault current limiter using a tuned LC circuit shunted by a MOV 7 

11.5 Power system network with SC 8 

11.6 Power system network during the source side fault with compensation 9 

11.7 Network model and phasor diagram under the prefault condition 10 

II. 8 Network model and phasor diagram under the load side fault condition 10 

II.9 FCL using power electronic switches (a) Short Circuit Current Limiter (SCCL), (b) 
Solid-State Fault Current Limiter (SSFCL) 12 

III. 1 Shunt compensation with a current source (a) Network configuration, (b) Phasor 
diagram: Vr can be controlled Vr to V'Rby compensating the reactive component of the 
load current 13 

111.2 Series compensation with a voltage source (a) Network configuration, (b) Phasor 
diagram: V R can be controlled by inserting Vcomp and the appropriate magnitude control 
ofVcoMP 14 

111.3 Equivalent circuit of single-machine infinite bus system: a generator delivers power 
to an infinite bus through two transmission circuits 17 

111.4 Power-angel curve for Equal Area Criterion 17 

111.5 A practical configuration of TCSC 18 

111.6 Impedance characteristics of a TCSC with respect to firing angle 19 

111.7 The characteristics of SCCL and power-angle curve (a) During normal operation, 
equivalent impedance is treated as zero and XL during the fault (b) Accelerating power is 
decreased as much as the hatched area by inserting the series reactor 20 

IV. 1 Axes of reference frame 23 



vin 



IV. 2 Voltage and current waveforms when duty ratio is where the current flows only 
through the series reactor, (a) Load voltage (b) Current 27 

IV. 3 Voltage and current waveforms when duty ratio is 1 where the current flows only 
through the bypass switch, (a) Load voltage (b) Current 28 

V. 1 Model for circuit analysis (a) Original circuit, (b) Equivalent circuit when switch is 
off, (c) Equivalent circuit when switch is on 30 

V.2 PI regulator with negative feedback 34 

VI. 1 Step responses of the plant: Uncompensated model has a steady state error (0.4651), 
which is eliminated by a PI controller where Kp=0.8, Ki=100 38 

VI.2 Overall model configuration and the output voltage responses: the output voltage 
changes from about 245kV to 270kV based on the duty ratio which starts to increase 
from0.5sec 39 

VI.3 Typical power system model to investigate the effects of TCSR on fault currents 
and voltage dips: faults can be occurred either near the TCSR or far away from it 40 

VI.4 Simulation results for the fault near the TCSR: The TCSR is required to be operated 
as fault current limiter and voltage restorer, (a) The bus voltage is operating in low level 
when the series reactor is inserted, (b) The fault current is exceeding the nominal value 
when the series reactor is bypassed, (c) Voltage is maintained higher and the fault current 
is limited within nominal value when the control scheme is applied 42 

VI.5 Simulation results for the fault far away from the TCSR: The TCSR is required to be 
operated as voltage restorer, (a) The bus voltage is operating in low level when the series 
reactor is inserted, (b) The voltage is maintained higher and the fault current is in low 
level when the series reactor is bypassed, (c) Voltage is maintained higher and no control 
action is required to limit the fault current 43 

VI.6 A 345kV transmission network for the voltage stability simulation: three substation 
buses can be reconnected when the TCSR is installed 44 

VI.7 P-V curves during normal and contingent conditions: maximum incremental 
transfer is increased from 300MW to 475MW when the TCSR is used 45 

VI. 8 Power angle curve for Equal Area Criterion: power system synchronism can be 
maintained when the accelerating power is smaller than the decelerating power and 
inserting the series reactor decreases the accelerating power as much as the hatched area. 
46 

VI.9 Network configuration for the transient stability simulation: a FCL using 
permanently-inserted series reactor is installed on a substation and two contingency cases 
(Fl, F2) are studied to analyze the influences of the FCL on the power system angle 
stability 47 

ix 



VI. 10 Simulation results on Fl fault: the power system can maintain synchronism with 
the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage [P.U.] 49 

VI. 1 1 Simulation results on F2 fault: the power system can maintain synchronism with 
the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage [P.U.] 50 



LIST OF EQUATIONS 
Equation 

II. 1 Equation for system voltage drop 3 

11.2 Equation for the current increase 5 

11.3 Equation for the receiving end voltage 7 

11.4 Circuit equations 7 

11.5 Injection voltage equation 8 

11.6 Current and voltage equations under the prefault condition 9 

11.7 Current and voltage equation during the fault 9 

III. 1 Voltage equation for simple AC circuit 15 

III.2 Voltage equation for the series compensated AC system 15 

III. 3 Relationship between the rotor angle and the accelerating power 16 

III.4 Equivalent impedance of TCSC 19 

IV. 1 Transformation matrix 22 

IV.2 Column vector and transformation matrix 23 

IV.3 Conversion variables in different reference frames 24 

IV.4 Conversion variables in the stationary reference frames 24 

IV.5 Conversion variables in the synchronous reference frames 25 

IV. 6 Space vector represented by three-phase components 25 

IV. 7 Space vector in the stationary reference frame 26 

IV. 8 Transformation to other reference frame 26 

IV. 9 Individual variables f a , ft,, f c 26 

V.l Voltage and current equations in case the thyristor switches are open 29 

V.2 Voltage and current equations in case the thyristor switches are close 31 



XI 



V.3 Averaged voltage and current dynamic equations 32 

V.4 Linearized function 32 

V.5 Dynamic model including steady-state term and linear small signal term 33 

V.6 Linearized small signal dynamic model 33 

V.7 Control transfer functions 34 

V.8 Control transfer function for the plant model 35 

V.9 A PI compensator model 35 

V.10 Closed-loop transfer function 35 



xn 



CHAPTER I 
INTRODUCTION 

Introduction 

Demand on electricity has been increasing tremendously and many countries 
invest significant amount of money for reliable power supply. More generation plants and 
transmission lines were constructed and the power systems became more complex. Major 
transmission lines tend to be long-distance and generation sites are large-scaled. Load 
concentration requires more transmission lines to be interconnected. However, those 
characteristics of power systems have been causing problems related to fault currents and 
system stabilities. 

Several approaches to cope with the fault current problems are being used in 
distribution and transmission areas. Permanently-inserted series reactors, up-rating and 
replacement of switchgear, splitting buses or transmission lines are the most commonly 
used techniques to limit the fault current in power systems, which are regarded as cost- 
effective and more secure measures for the operational reliability of power system 
facilities. However, up-rating and replacement of switchgear can be very expensive and 
short-circuit current duty may not be reduced. Network splitting can deteriorate the 
power system security. Permanently-inserted current-limiting series reactors introduce a 
voltage drop, active and reactive power losses and also adversely affect the power system 
stability. In spite of these drawbacks, a lot of power systems are still divided into several 
subsystems to solve fault current problems. 

For the power system stability enhancement, on the other hand, the following has 
been used as countermeasures in general: (1) Constructing more interconnection lines, (2) 

1 



Installing dynamic reactive resources, (3) Constraining power transfers, and (4) Using 
Special Protection Schemes (SPS). 

So far, fault current and stability analysis has been studied separately, since 
network configuration influences in an opposite way to those problems. When 
transmission systems are fully meshed, they tend to yield fault current problems, rather 
than stability problems. On the other hand, when powers are delivered through high 
impedance transmission lines, stability issues may arise instead of fault current problems. 
However, as the power systems become more complex with the meshed transmission 
networks which are interconnected with long-distance, high-power transfer transmission 
lines, those two problems become co-existent. Consequently, countermeasures to deal 
with the fault current impact more on the power system stability than before. 

In this work, prior researches related to fault currents limitation and power system 
stability enhancement are reviewed and a TCSR that limits the fault current and improves 
the stability simultaneously is presented. The influence of the TCSR from the perspective 
of voltage security enhancement is shown with a theoretical analysis, and to assess the 
feasibility of the TCSR to real power systems, the benefits of the TCSR are demonstrated 
with bulk power system simulation results. 



CHAPTER II 

FAULT CURRENT LIMITERS 

Fault current limiters can be applied in a variety of distribution and transmission 
areas. Those can be used for the protection of entire bus or individual circuit as in Figure 
II. 1. For the last 20 years, super-conductive FCLs have been studied and suggested to 
limit the fault current, but they have not been used widely in the field because of the cost 
problem. Reactors, high impedance transformers, circuit breaker upgrades and splitting 
buses or transmission lines are still widely used. Because of the fault current problem, 
many power system operators are sacrificing their system reliability by splitting the 
network into many sub- systems. However, comparing to the Superconductive FCL, these 
methods have many disadvantages with respect to transmission losses and system 
reliability. Many alternative ways to overcome those problems have been suggested. 

Fault Current Limitation by a Series Reactor 

Most commonly used FCLs are permanently-inserted series reactor type fault 

current limiters. As this type of fault current limiter does not require replacement of 

switchgear and more economical than others, it is commonly used in power systems. The 

fault current driven by the voltage source is reduced by the impedance of the reactor. 

AV 1 

= 1- 



V, 



Jl + 2lWl-cos 2 + v k 7 
Equation II.l Equation for system voltage drop. 




Figure II. 1 Fault current limiter application: it protects the entire bus or individual 
circuit. 

However, it may cause severe voltage drop during contingent state, while the system 

voltage drop may not represent a particular problem during normal operating conditions 

[1]. The system voltage drop can be calculated using the following equation and Figure 

II.2 shows the relationship between system voltage drop, reactor short-circuit voltage Vk, 

and power factor. 



Bypass Switch 

In the 1980s, most power systems were operating with splitting network topology 
such as splitting buses or opening transmission lines at normal operating conditions to 
limit the fault current. A tuned-circuit impedance method was proposed to limit the fault 
current by Electric Power Research Institute (EPRI) [2]. Figure II.3 shows the basic 
configuration of this circuit. Under normal operating conditions, the switch is opened and 
transmission line has zero net impedance if they are tuned properly. When a fault occurs, 

x 2 
the switch is closed and the equivalent impedance becomes — where X is the impedance 



of the reactive components, which results in fault current reduction. Although it requires 
high initial cost, its zero net impedance during normal operating conditions can reduce 
the operating cost such as transmission loss; besides, the system voltage recovers to its 
prefault level after clearing the fault. 



AV 

V7 



[%] 




co5<r>= 


«.6 


cos<D=0.7 


C05<J>= 


=0.8 


COS<J> 


=0.9 


C05<I>= 


=0.95 



cosO=l 



V k [%] 



Figure II.2 Relationship between system voltage drop, reactor short-circuit 
voltage and power factor. 

Tuned LC Circuit Shunted by a Metal Oxide Varistor (MOV) 

This type of FCL was developed for the fault current limitation and power quality 
improvement [3] . It consists of a series LC circuit tuned at the system frequency and a 
MOV in parallel with the capacitor as shown in Figure II.4. Since the LC circuit is well- 
tuned, it is almost transparent during normal operation. When there is a fault in the 
downstream of the FCL, it forces a gradual increase of the current, which is justified by 
the following equations. 

1 11 

i(t) = V P [-sm(wt + 6-8) -\ sin0sinwt H wtsin(wt + 0)1 

Z 2wL 2wL 



Equation II.2 Equation for the current increase. 



Where, V P : magnitude of the source voltage, 0: phase angle of the source voltage, Z: the 
magnitude of the load impedance, 5: load angle. 





II 





Figure II.3 Fault current limiter with tuned impedance. 

This shows that the higher the L, the slower the current increase, which reduces the 
voltage sag during the fault. However, since the voltage on the L and C will increase 
during the fault, additional device to limit the over-voltage is required. MOV is 
connected in parallel with the capacitor, and it absorbs the excessive energy in case its 
protection level is reached. However, long cool-down time of the MOV and possibility of 
Sub-Synchronous Resonance (SSR) [4] are the drawback to be solved. 



Series Compensator 

Dynamic voltage restorer (DVR) using energy storage device and a series 
compensator (SC) shown in Figure II.5 was proposed to limit the fault current and 
improve the voltage quality of the power system [5, 6]. By controlling the amplitude and 



phase angle, they control the real and reactive power between the controller and the 
power system. 





Figure II.4 Fault current limiter using a tuned LC circuit shunted by a MOV. 



by 



During normal operating conditions where the receiving end voltage Vl is given 



V L = V s -jX s I L 



Equation II.3 Equation for the receiving end voltage. 

, the SC does not operate. However, when there is a fault in the network, it compensates 
the voltage by injecting a lagging or leading voltage in quadrature with the load (fault) 
current to restore the line voltage and limit the fault current. Considering a fault at the 
source side, the voltage of the source will be dropped, and the circuit equation becomes 



Without compensation : V PF = V' L = V SAG —jX s I' L 



With compensation : V L = V SAG —jX s I L + V sc 



Equation II.4 Circuit equations. 



Where V' L , I' L and V PF are the load side voltage, line current, and SC side voltage vector 
during the fault respectively. 





jx s 






Series 
Compensator 





Filter 



VSI 



Hh 



V, 




JX L 



-£>Load 



Figure II.5 Power system network with SC. 



To enhance the voltage drop, the SC injects a lagging voltage V sc until the load side 



voltage is restored to its prefault level V L as shown in Figure II.6. Since V SAG — jX s I L is 
the voltage on the source side of the SC and if we set V L = V P , then the injection voltage 



V sc becomes 



V qr = V P - V 



v sc 



PF 



Equation II.5 Injection voltage equation. 



V'p F : measured voltage on the source side of the Series Compensator (SC). By injecting 
a lagging voltage, we allow the DVR to restore the load side voltage to its pre-defined 



level under normal and contingency conditions. On the other hand, if the fault occurs at 
the load side, the SC should act as a fault current limiter. 




V' L 



I'l 



-[>Load 



JX L 



V 



SAG 



Figure II.6 Power system network during the source side fault with compensation. 



The current and voltage equations under the prefault condition can be expressed as 



V s -V P -jX s I L = 

%-%-ixT L = o 



Vs-Vp 
JX S 



Equation II.6 Current and voltage equations under the prefault condition. 



, and the system model is shown in Figure II.7. During the fault where the V F = 0, those 
equations become 

%-Vp~;-jx s r L = o 

Vp~* F -jxT F = o 

v s -vp~; 



h = 



JX S 



Equation II.7 Current and voltage equation during the fault. 



From the comparison between equation II.6 and equation II.7, we see that the fault 
current can be limited to the load current when V PF is restored to V P . The SC injects a 
leading voltage V sc until V PF is restored into its prefault level V P as shown in Figure II. 8. 





JX 3 



k 



jx 



w — w — >- 



j(X L -X) 




Figure II.7 Network model and phasor diagram under the prefault condition. 




^ t>Lo a d 

^ KX L -x) 



\\ 




Figure II.8 Network model and phasor diagram under the load side fault condition. 



10 



Power Electronic Switches 

A great deal of power electronics based FCLs have been proposed for fault 
current limitation and power system stability enhancement. With the development of 
power electronic devices and control technologies, a large number of Flexible AC 
Transmission Systems (FACTS) devices have been developed and are in operation 
extensively for the security enhancement of power systems [7]. FCLs using solid-state 
devices such as Insulated Gate Bipolar Transistor (IGBT), Silicon Controlled Rectifier 
(SCR), and Gate Turn-off Thyristor (GTO) can be classified into (1) Series Switch type 
FCL, (2) Bridge type FCL, and (3) Resonant FCL [8]. The basic operational principle of 
SSFCLs is almost same in that currents flow through zero impedance path in steady-state 
and they are switched into the fault current limiting reactor in case of short-circuit 
conditions. However, the configuration of SSFCLs can be different based on their 
application purpose. Different types of Series Switch type FCLs were described [9] and 
an application of a Thyristor-Controlled Series Reactor was presented to reduce furnace 
arc flicker [10]. Bridge-type FCLs using different types of switching device were also 
proposed [11, 12], and the influence of this type of FCL was investigated in terms of 
power system transient stability [13]. Another application using FACTS based Short- 
Circuit Current Limiter (SCCL) was suggested in [14], where thyristor Protected Series 
Compensator (TPSC) combined with an external reactor showed the benefits for fault 
current limitation and SSR mitigation. Transient stability was also evaluated with this 
type of series capacitor compensated FCL in [15]. Basic configurations for those FCLs 
are illustrated in Figure II.9. 



11 



SCCL 




(a) 



SSFCL 




(b) 



Figure II.9 FCL using power electronic switches (a) Short Circuit Current Limiter 
(SCCL), (b) Solid-State Fault Current Limiter (SSFCL). 



12 



CHAPTER III 

POWER SYSTEM STABILITY 

For the voltage and reactive power compensation, we usually use reactive power 
compensator such as static condensers, shunt reactors which are static reactive sources 
being used for steady state voltage regulations and thyristor controlled series condensers, 
thyristor controlled reactors which are dynamic reactive sources being used for transient 
stability enhancement. 




V, 



X 




R 



Vr 



(a) 




JX-Ip 



(b) 



Figure III.l Shunt compensation with a current source (a) Network configuration, 
(b) Phasor diagram: Vr can be controlled Vr to V'Rby compensating the 
reactive component of the load current. 



13 




X 



R 



V 3 



v E 



(a) 




(b) 



Figure III.2 Series compensation with a voltage source (a) Network configuration, 
(b) Phasor diagram: Vr can be controlled by inserting Vcomp and the 
appropriate magnitude control of Vcomp- 



They can be connected to the system in series or in shunt. To reduce transmission losses 
and improve the voltage regulation and stability, we normally compensate reactive 
powers near the load. By injecting the reactive component of the current near the load, a 
compensator can control the current from the generator resulting in voltage regulation 
improvement in the load side. Considering leading compensation, we can increase the 



14 



load side voltage to V'r with the same source voltage Vs. In addition, we can reduce 
relatively large amount of reactive losses compare to uncompensated system. Therefore, 
this kind of compensation is usually used for voltage stability enhancement. Figure III. 1 
shows the principle of shunt reactive power compensation in a simple AC circuit which 
can be represented as 

V s = V R +I P (R+jX) 

Equation III.l Voltage equation for simple AC circuit. 

Based on the compensation types required, inductors or capacitors can be used. For 
independent control with the voltage at the connection point, current source or voltage 
source compensator can be used [16]. Var compensation can also be realized using series 
compensator. Typical series compensation is made by series capacitors and Figure III.2 
shows the principles of series compensation in a radial AC system which can be 
represented as 

V s = V' R +I P (R+jX)-V C0MP 

Equation III.2 Voltage equation for the series compensated AC system. 

The voltage angle of V' R can be changed by inserting Vcomp between the line and the 
load. With the appropriate magnitude control of Vcomp, V r can be controlled. This kind 
of series compensation gives three main benefits to the transmission system. (1) Increase 
angular stability of the system (2) Improve voltage stability of the system (3) Optimize 
power sharing between parallel circuits. Equal Area Criterion is generally used to 
understand basic factors that influence the transient stability of power systems [17]. It 
basically uses the relationship between the rotor angle and the accelerating power. 

15 



d 2 8 w 

~d^ = 2H {Pm ~ Pe) 

Equation III.3 Relationship between the rotor angle and the accelerating power. 

Where, Pm: mechanical power, P E : electrical power, 8: rotor angle, in electrical radian, H: 
inertia constant, in MWs/MVA. Let us consider the response of single-machine infinite 
bus system to a three-phase fault on transmission line2, as shown in Figure III.3. Network 
conditions can be represented as: (1) Prefault (both circuits in service), (2) During a 
three-phase fault, (3) Postfault (circuit 2 out of service) and those are illustrated with P-8 
plots in Figure III.4. Initially, the system is operating where Pm = Pe- When the fault 
occurs, P E goes down to b. At this point, since P M is greater than P E , the rotor starts to 
accelerate until the fault is cleared. When the fault is cleared, the operating point shifts to 
d based on the line condition. However, since the rotor speed is greater than the 
synchronous speed, it continues to increase until the kinetic energy gained during the 
acceleration period is exhausted. The operating point moves to e, where the accelerating 
power is equal to the decelerating power. At point e, the rotor speed is equal to the 
synchronous speed, but P E is greater than P M . Therefore, the rotor starts to decrease the 
speed following the P-8 curve for the single circuit condition. In the presence of any 
source of damping, the rotor finally gets to a new stable operating point. With a delayed 
fault clearing, acceleration power is greater than deceleration power, leading to loss of 
synchronism. 



16 




E'aS 



l 21 





X 



22 




£f^Q 




Figure III.3 Equivalent circuit of single-machine infinite bus system: a generator 
delivers power to an infinite bus through two transmission circuits. 

Generator 
output Power 



Q.ouble Circuit Condition 



Pm=Pp 




A.P : Acceleration Power D.P : Deceleration Power 



Sicgle Circuit Condition 



Faulted 
Condition 



Power Angle 



Figure III.4 Power-angel curve for Equal Area Criterion. 

Thyristor Controlled Series Compensator (TCSC) 

A typical TCSC consists of a Fixed Series Capacitor (FC) in parallel with a 
Thyristor Controlled Reactor (TCR). The bi-directional thyristor valves are red with a 
phase angle ranging between 90 and 180 with respect to the capacitor voltage. A Metal- 



17 



Oxide Varistor (MOV) is used to prevent the over-voltage across the capacitor. A circuit 
breaker is installed across the capacitor and it bypasses the capacitor when severe faults 
or equipment-malfunction events occur. Conduction losses of the TCSC valves can be 
minimized by installing an Ultra-High-Speed Contact (UHSC) across the valve. It is 
closed shortly after the thyristor valve is turned on, and opened shortly before the valve is 
turned off. During a sudden overload of the valve and fault conditions, the metallic 
contact is closed to alleviate the stress on the valve [18]. 




CB 



MOV 



UHSC 






^f^r- 



Figure III.5 A practical configuration of TCSC. 

Figure III. 5 shows a practical configuration of TCSC. The main capabilities of the TCSC 
can be achieved by changing the impedance of the line where it is connected, which can 
be done by controlling the firing angle of the thyristors. Variation of Xl with respect to 
firing angle and the equivalent impedance of the TCSC are given as the following 



equations 



*l(<x) = *l 



TT 



n — 2a — 2sin2a 



,X L <X L (a)<oo 



18 



^TCSC\ a ) — X c 



X, 



Xr Xr 



2 o + sino AX C 2 cos 2 ( 7 ) ktan (-5-) - tan(a 2 ) 

X + X— : S_X ^-^ 

X, n X r - X, k 2 - 1 n 



Equation III.4 Equivalent impedance of TCSC. 

Where, o = 2(7t-a) is the conduction angle of TCSC, and k = I— is the compensation 

ratio. Figure III.4 shows the impedance characteristics of a TCSC. 
The folio wings represent the main functions of a TCSC. (1) Damping of the power 
swings from local and inter-area oscillations, (2) Suppression of subsynchronous 
oscillations, (3) Voltage support, and (4) Reduction of the short-circuit current. 



Inductive Region j 


i 


7 










ss**\ 


' 




Resonance Region — <^ 


Capacitive Region 



► a 



Figure III.6 Impedance characteristics of a TCSC with respect to firing angle. 



19 



Short Circuit Current Limiter (SCCL) 

SCCL is developed from the series compensation which normally uses a capacitor 
to compensate the inductor used as a fault current limiter, thus the line is regarded as 
short-circuited. During normal operation, the FCL compensated with series capacitor 
increases the steady state stability limit. When a short-circuit fault occurs, the FCL can 
reduce the accelerating power at the initial stage of the fault and provide additional 
decelerating power at the fault clearing stage [15]. 



o 



Fault 



Clear Fault 



(a) 



Generator 
output Power 




A.P : Acceleration Power D.P : Deceleration Power 



Double Circuit Condition 



ingle Circuit Condition 



FCL Operation 

Condition 

Faulted 

Condition 
Power Anele 



(b) 



Figure III.7 The characteristics of SCCL and power-angle curve (a) During normal 
operation, equivalent impedance is treated as zero and XL during the fault (b) 
Accelerating power is decreased as much as the hatched area by inserting the 
series reactor. 



20 



Figure III.7 shows an example of a single line fault where double circuit transmission line 
becomes single circuit transmission line. The accelerating power will be decreased as 
much as the hatched area and power system synchronism can be maintained if the 
resultant accelerating power is smaller than the decelerating power. 



21 



CHAPTER IV 

D-Q TRANSFORMATION 

We transform time-varying voltage, current differential equations into time 
invariant differential equations. As it is not only easy to solve but also easy to understand 
and control. A, B, C phase variables in three phase AC system are transformed into 
orthogonal d, q, n axes variables [21]. Direct axis d represents the axis where excitation 
flux (or main flux) is and quadrature axis is 90 degree in electrical angle ahead to d axis 
in positive rotational direction and neutral axis is orthogonal to d-q axes in three 
dimensional spaces. Figure IV. 1 represents axes of reference frames, where superscript s 
denotes stationary reference frame, e synchronous reference frame, w arbitrary rotating 
speed and is defined as 

0= [w(f)df+ 6(0) = [wtf)d£ 

''O -'0 

The transformation matrix can be derived as 

fdqn = T(B)f a b c 

Equation IV. 1 Transformation matrix. 

The column vectors of variables are given as 

fW r fW fw fWiT 

Jdqn Yld Jq Jn 1 

fabc = [fa fb fc] 



22 



ne) = 3 



cosQ cos ( 6 TT } cos(6+- 

3 / V 3 

-sinQ ~sin(6— -tt) — sin(6 + 



1 



-v) 

1 



Equation IV.2 Column vector and transformation matrix. 



-) 
I-) 



1 



imaginary axis 




* real axis 



Figure IV.l Axes of reference frame. 

The variables in the three -phases axis can be converted both to the variables in the 
stationary reference frame and to the variables in the arbitrary reference frame as 

fdqn = T(Q)f a bc 
fdqn = nVfabc = R(VnO)fabc = R(Vf<? q n 



23 





1 


1 1 
~2 ~2 


7(0) = § 





V3 V3 
~2~ ~T 




1 


1 1 




- V^ 


V2 V2 


r 


cosB 


sinG " 


i?(6) = 


—sinB 


cosG 


. 





1-1 



T(6) = i?(9) T(0) 
Equation IV.3 Conversion variables in different reference frames. 

If the system is balanced, that is f a + f b + f c = 0, and convert the variables in the three- 
phase axis to the variables in the stationary reference frame, then 





f 


dqn — T(0)f abc 

r iii 




\fi] 
n 

fn S . 


2 
~3 


1 "2 "2 

V3 V3 

t -T 

111 

- V2 V2 V2 - 


"/a" 
/ft 

/c 


fi 


2 11 

~~ q \Ja ~ ^ Jb ~ ~^Jc) ~ J a 






f s _ 7ft /c 





' q V3 

Equation IV.4 Conversion variables in the stationary reference frames. 

Likewise, the variables in the synchronous reference frame can be converted with respect 
to the stationary reference frame as 



24 



n 

f q e 

fn 6 



fdqn — R(.®e)fdqn 



cosB e sinB e 
—sinB e cos& c 











0" 


f/cfl 





U 


1 - 


M. 



fd = fd cosB e + f q s sinB e 

fq = ~fd sinQ e + fq S COSB e 

Equation IV.5 Conversion variables in the synchronous reference frames. 

As a result, when the space vector by three-phase components can be represented as the 
equation IV. 7, three-phase variables can be represented by only two orthogonal 
components of a complex vector. 



fabc = 3 (fa + afb + a 2 fc) 



fn= 2<Ja+fb+fc) 



,■2 2 2 1 V3 

a = e-'s = cos-n + isin-Ti = — — + /-— 
3 ' 3 2 J 2 



Equation IV.6 Space vector represented by three-phase components. 

2 11 H 

The real part of f abc equals to -(f a — f b — f c ) which is correspondent to f s and the 

imaginary part of f abc equals to - ( — f b f c ) which is correspondent to f s q . 

Consequently, the equation to transform a space vector fabc to the space vector in d-q 
axes which are stationary can be expressed as 

fdq — fd + Jfq = fabc 

fd = real(f abc ) 



25 



f q s = imag(f abc ) 
Equation IV.7 Space vector in the stationary reference frame. 

Likewise, from the previous relationship between the synchronous reference 
frame and stationary reference frame, and using Euler equation and basic vector 
modification, we can derive the transformation to other reference frame as 

fi q = fa +jf q e = fi q e- je * = fa bc e- ]e ° 
Equation IV.8 Transformation to other reference frame. 

Inversely, we can extract the individual variables fa, fb, fc from the space vector f a t, c . 

2 2 1 1 

real(f abc ) = g (/a + af b + a z f c ) = -f a - -f b - -f c 

2 , 7 N 1 2 1 

real(a z f abc ) = -{a z f a + f b + af c ) = --f a + -f b - -f c 

2 112 

real(af abc ) = -(a/ a + a z f b + f c ) = --f a - -f b + -f c 

fn= \(fa+fb+fc) 

f a = real(f abc ) + f n 

f b = real(a 2 f abc ) + f n 

f c = real{af abc ) + f n 

Equation IV.9 Individual variables f a , 4, f c . 

This approach is demonstrated with a specific R-L circuit shown in Figure V. 1 (a) and 
parameters used in Table VI. 1. Following figures are the voltage and current responses 
with respect to different duty ratios. 



26 



x 10~ 



Three phase signals 




0.1 



x10' 



0.12 0.14 0.16 

stationary reference frame 



0.18 



0.2 









I 






/""v 




! I 


— 




V i 






i "\ \'f X rT / 
V \ / / V\ / 










Vds2 ij 




\ \ A / V \ / 




_ L..V.J \ 








- ^**f y&*s 






-x^ r*-^>n 



x 10 



0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 
- synchronous reference frame 



3r 

2 

1 



-1 



— -f- — 


- — 1— — (— H 




"*■"■" — ■■■ 










... ...... ,.. 










1 

_ 1 _ 


- - 1- - i- - 


— — - 


— — 








■ — — 




32 
32 




Vd< 




■ Vq< 







...._ 




1 




i i 


' 










i 



0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 



(a) 



Three phase signals 




0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 

stationary reference frame 



5000 



-5000 



6000 

4000 

2000 



-2000 



y 








-/^V^ 1 


— Y 


/\\ 


/ f\ \ 




Id 


.< 














V._/.. i ...\_.v_ 




|L i 




._ IVy 
















V^Xjr j VA, 


r~ \ss\~* 



0.1 0.11 0.12 0.13 0.14 0.15 0.16 0. 1 7 0.18 0.19 0.2 
synchronous reference frame 













1 , 












™ 


Ide 








j 










I 
















I 


: 








i i 



0.1 



0. 12 



0.14 



0.16 



0.18 



0.2 



(b) 



Figure IV.2 Voltage and current waveforms when duty ratio is where the current 
flows only through the series reactor, (a) Load voltage (b) Current. 



27 



x 10~ 



Three phase signals 



















l"^ ^^ 


J-^ J*1 


w -, (■ 












Va1 








\[ \f j y y 




\^/\_^ 


J^^A^ 


VO I ^ 


" Vc1 












y v/ jv ^ 



X 10 



O.I 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 

stationary reference frame 



x 10 























\J 
















\ 


F VcJti 1 
- Vqs1 - 












/ M V / > 


s 


















' v^-^ 



0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 
: synchronous reference frame 





' 








1 


! F 




i 




! 




E 


Vde1 




j 




1 




E 


\/qe1 




I 




i 




1 




1 

1 




1 




1 




■ 




E 

■ 



0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 



(a) 



Three phase signals 




0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 
stationary reference frame 













u^TN-OsL J 






~ i j 


1 1 




t 




I / 




-/—/- 


f f\ \ / 


r \ V 




\ fjr 


Ids ^ 





Iqs - 


5000 


N y a 










jV^ v^ 








\A>S\ 



8000 

6000 

4000 

2000 

O 

-2000 



O.I 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 
synchronous reference frame 











; i 








i i 






















I 























- - 


- — - 











--}— 





J 

i 


















Ide 


Iqe 


















f 




[ 












! 










1 








i 










I i 








' 



0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 



(b) 



Figure IV.3 Voltage and current waveforms when duty ratio is 1 where the current 
flows only through the bypass switch, (a) Load voltage (b) Current. 



28 



CHAPTER V 

PROPOSED APPROACH 

In order to demonstrate the advantages of the TCSR, especially from the voltage 
point of view, a simple R-L circuit shown in Figure V. 1 (a) is used. The receiving-end 
voltage is controlled by changing the equivalent impedance of FCL. To achieve this goal, 
following approach is proposed. A state-space model is constructed and averaged using 
d-q transformation method. Since the input (duty) and output (vr) variables feature 
nonlinear relationships, linearization technique is applied to the averaged state-space 
model to obtain a system transfer function. A PI controller is designed to get a better 
dynamic response and zero steady- state error. 

Voltage Stabilizing Fault Current Limiter 

When the thyristor switch is open, the network in Figure V. 1 (a) becomes as 

shown in Figure V.l (b) and the voltage and current dynamic equations are given as 

( dTl _, dTl _, 

v s ~ L T —— — Rt 1 l~L fcl —— = R L i L 

d? L R+ jw(L T + L FCL ) -> vf 



ll + 



at (L T + L FCL ) (L T + L FCL ) 

Equation V.l Voltage and current equations in case the thyristor switches are open. 

x e = xe~ Jwt , R — R L + R T , and the superscript e denotes synchronous reference frame. 
When the switch is closed, the network becomes like Figure V.l (c) and the voltage and 
current dynamic equations become 

29 



^^ 








R_ 



(a) 




y^^^A 



Lt 



R- 



FCL 



V„ 



(b) 




R L 



(c) 



Figure V.l Model for circuit analysis (a) Original circuit, (b) Equivalent circuit 
when switch is off, (c) Equivalent circuit when switch is on. 



30 



dTi _^ dii 
— -R TlL -L EQ — 



v s ^t~TT Rt 1 l L E q —j2 — Rl 1 l 



dij _ R+jw{L T + L EQ ) -* v e s 

ut \L T + L E q) \L t + L E q) 

Equation V.2 Voltage and current equations in case the thyristor switches are close. 

Leq = LfclLtcr/(Lfcl+Ltcr)- These equations can be arranged into a set of state 
equations as 

x = Ax + Bu 
y = Cx + Du 
Where, x: state variable, u: input variable, y: output variable. 
As the average behavior of the system is dependent on the conduction time of the 
thyristors [19], if we define the conduction and off-conduction time as T T and T B 
respectively, we can rewrite the previous equations into two sets of state equations 
depending on the different conduction stages 

x' T = (A T x + B T u)T T 
x' B = {A b x + B b u)T b 
Where Ts = T T + T B : switching time, and subscript T and B denote ON and OFF, 
respectively. The averaged model for the system can be expressed as the following set of 
state equations 

x = (A T d T + A B d B )x + (B T d T + B B d B )u 
= A T x + B T u + d{A B - A T )x + d{B B - B T )u 
y = C T (1 — d)x + dC B x 

31 



d T = T T /Ts = 1-d, d B = T B /T S = d 
Applying this relationship into the system model equations V.l, V.2, then, 

R +jw{L T +L FCL ) 



di e , 


R +jw(L T +L FCL )-, v e s 




li I 


dt 


{L T + L FCL ) (L T + L FCL ) 



+ d{- 



(L T + L FCL ) 



R + jw(L T + L E0 ) — 1 1 — 

Equation V.3 Averaged voltage and current dynamic equations. 

As a result, the voltage drop on the fault current limiting reactor can be limited by the 
following factor and controlled by duty d. 

R + jw(L T + L FCL ) R +jw(L T +L E0 ) — 1 1 — 

d ^ — _y_w — fcl± _7_^t — ^LLy L + d{- ^ - -}v< 

{L T + L F cl) [L T + L E q) [L t + L E q) (L t + L FCL ) 



Plant Model and Compensator Design 

However, the system model is nonlinear because the duty is also a function of 
time. Therefore, we need to linearize the non-linear equation to solve. Considering non- 
linear function F{Z) and applying Taylor formula at Z = Zo, the linearized function can 
be approximated as 

dF 
F{Z)~ F(Z ) + — (Z-Z ) 

Equation V.4 Linearized function. 



For the controller design, we define state variable, input, and output vector as 

x = [Til u = * , y = \y£\ 



32 



, then the state equations can be written as 

x = F(Jl,v^,d) 

y = G{T L ,v* s ,d) 

If we apply linearization method at an operating point where steady state values are I L , Vs, 

D, V R , X, U, the dynamic model can be expressed with steady-state terms and linear 

small signal terms as 

d dF _ dF dF 

- iL = m ,U- )+ -( lL -I D+ —(v s -V s - )+ -U-D-) 

dG _ dG dG 

vZ = G(X,U)+ — (r L -I L )+ — (T s -V s )+ — (d-D) 
oi L dv s ad 

Equation V.5 Dynamic model including steady-state term and linear small signal 
term. 

From these equations, we get the following linearized small signal dynamic model of the 

system. 

d - dF _, dF _, dF _ 
dt oi L dv s dd 

_, dG^ dG _, dG _ 

VR= - d T L tL + dV s Vs + dd d 

h = h + ~k,v^ = ^ + %,d = d + D 
Equation V.6 Linearized small signal dynamic model. 

Rewriting the equations leads to the following form as 

i L = AT L + j%& + B^d 

i?= £f L + D^ s % + Fr d d 

, and applying superposition rule gives the following control transfer functions (v$ = 0). 

33 



h 



(sI-A^Ba 



A = 



Vr_ 

d 

R(D - 1) 



CdsI-A^Ba 



RD 



(L T + L FCL ) (L T + L EQ ) 

R(D - 1) 



w 



B, = 



RD 



-w 



(L T + Lfcl) (L t + L E q) 

'. R R }j 

\{L T + L FCL ) (L T +L EQ )j LD 



R 



R 



(L r + Lfcl) (Lt + ^eq). 
C = 



I 



LQ 



R L W 

-w R L 



Equation V.7 Control transfer functions. 




*V r 



Figure V.2 PI regulator with negative feedback. 

In the synchronous d-q reference frame, AC quantities can be treated as DC. In addition, 
by aligning the voltage vector to the d-axis, the output voltage of the q-axis can be set to 
zero. Therefore, substituting the equation V.7 with the derived values A, B d , C, we obtain 
the following transfer function. 



34 



Gvd(s) = 



Ki 



v Rd ^2RJlD s ~ K1K2RJLD + K 2 Rl1lQ w 


d s 2 - 2K t s + K t 


2 +w 2 


R 1 
+ RD{ 

L T + L FCL L T + L FCL 


1 
L T + L E q 


1 1 
K 2 = RCi—r-, ^—^ 


") 



Equation V.8 Control transfer function for the plant model. 

Our plant and compensator transfer function can be expressed with G v d(s) and G c (s) in 
Figure V.2. To improve low-frequency loop gain and regulation, a PI compensator is 
designed. 

Ki 

G c (s)= K P +j 

Equation V.9 A PI compensator model. 

The closed-loop transfer function is given as 

Vr T 



Vref 1 + T 

Equation V.10 Closed-loop transfer function. 

The loop gain T = G c (s)-G v d(s). 

Routh's Stability Criterion can be used to determine the ranges of coefficients of 
polynomials for stability [20] . Considering the characteristic equation of an nth order 
system, the Routh array can be arranged as the following form 



35 



H(s) = s n + ais"" 1 + a 2 s n " 2 +-" + a n _i s + a n 



Row n s n : 1 a 2 a 4 



Row n-1 s n_1 : ai a 3 a 5 



Row n-2 s n " 2 : bi 



Row n-3 s n " 3 : ci C2 C3 



Row 


2 




s 2 


Row 


1 




s 1 


Row 







s° 




h. : 


a a 


a 2 -a 3 



> h = 

_ Mj - a t b 2 _ b t a s - a t b 3 
Cl ~ b t >C2 ~ b x 

A necessary and sufficient condition for stability is that all the elements in the first 

column of the Routh array are positive and it is shown that it is true for equation V.8 and 

V.9. 



36 



CHAPTER VI 
COMPUTER SIMULATIONS 

Duty Control to Increase Output Voltage 

This approach is demonstrated with the R-L circuit shown in Figure V.l and 
parameters used for the simulation are shown in Table VI. 1 . The transfer function of the 
plant model can be derived from V.8, which is given as 



_ i%d 1204s + 1.261 x 10 6 



d s 2 + 2094s + 1.096 x 10 6 

It has a constant steady state error, because the plant model has a small value when s = 0. 

To eliminate the steady state error, we have designed PI compensator, which gives the 

open-loop transfer function as 

K, 1204s + 1.261 x 10 6 
T= (K P +A 



s J s 2 + 2094s + 1.096 x 10 6 
The characteristic equation of the close-loop transfer function as 

1 + T = s 3 + (2094 + 1204K P )s 2 + (1.261 x 10 6 K P + 1204K, + 1.096 x 10 6 )s 
+ 1.261 x 10% 
Applying Routh's Stability Criterion to the characteristic equation of the close-loop 
transfer function gives K P = 0.8 and Ki = 100. As a result, the PI compensated transfer 
function becomes 

963.5s 2 + 1.129 x 10 6 s + 1.261 x 10 8 



T = G c (s)G vd (s) 



s 3 + 2094s 2 + 1.096 x 10 6 s 
Steady state error is eliminated and the bus voltage can be enhanced by controlling the 
duty ratio of the TCSR. The output voltages are controlled from 245kV to 270kV based 



37 



on the duty ratio which starts to increase from 0.5sec. The step responses of the system 
and the output voltage responses with respect to different duty ratios are shown in Figures 
VI. 1 and VI. 2. Simulations are done with MATLAB. 



Table VI. 1 Simulation parameters 








Vs Rt Rl 


1_jJ 


Lfcl 


Ltcr 


345kV 0.82n 41.060 


0.015H 


0.025H 


0.00025H 



1 


1 


! 1 ! 1 I 

: : i l 


\ ■ 

] : 


0.8 




___ i 1 

jr \ j ^v j *■ * -4- 


i 
i 






* ^ Compensated model response 




L__. U.b 

T3 






3 

-I— 1 

"D. 

< 0.4 

0.2 

- 











i 

3 


— Undompen 


;ated model response 








1 
\ 

\ 
1 

1 


t 

: 

\ 
t 


( \ 







0.01 0.02 0.03 



0.04 _ 0.05 _ 0.06 

Time[sec] 



0.07 0.08 0.09 



0.1 



Figure VI. 1 Step responses of the plant: Uncompensated model has a steady state 
error (0.4651), which is eliminated by a PI controller where K P =0.8, Ki=100. 



38 



>.7. 



—*Q 



* 



■nr ijb 



□ 




?'■:: 



(a) 



23 

2.75 
> 


K 10 




























































£ 2.7 

- 

> 2.65 
2.6 

2.55 

2.5 

2.45 

.1 

































































































































C.2 



3.4 



: 6 



Co 



1.2 1.4 1.6 1.8 2 

Time[sec] 



(b) 



Figure VI.2 Overall model configuration and the output voltage responses: the 
output voltage changes from about 245kV to 270kV based on the duty ratio 
which starts to increase from 0.5sec. 



39 



Effects of TCSR on Different Fault Locations 

Because the network is more complex than the simple R-L circuit in Figure V. 1 
(a), we need to consider faults that occur at different locations, e.g., near or far from the 
TCSR. When the fault occurs near the TCSR, the fault current will be high and the 
voltage will be low. Then the TCSR is required to operate as a fault current limiter and 
voltage restorer. On the other hand, when the fault occurs at a location far away from the 
TCSR, both the fault current and the voltage will be low. Then it does not need to act as a 
fault current limiter, but as a voltage restorer. This has been shown by PSCAD/EMTDC 
model shown in Figure VI.3. 




r® ^WW 1 — zn — -n 

L® 0.15 8.2 3* "-©©Hi. 



LOAD 



) L~ 

■ a 



SOURCE 







Figure VI.3 Typical power system model to investigate the effects of TCSR on fault 
currents and voltage dips: faults can be occurred either near the TCSR or far 
away from it. 



The fault current is confined within nominal short-circuit current level with the series 
reactors and voltage drop due to the series reactor is around 4% which can be derived 
from the following equation [1]. 



AV 



1- 



Jl + 2lWl-cos 2 +V k < 



40 



, where, — : system voltage drop, Vk: reactor short-circuit voltage, and cosO: power 

v N 

factor. In this system, possible issues are fault current problems in case the faults occur 
near the TCSR and under-voltage problems when the faults occur far away from the 
TCSR. Control actions of the TCSR enhance the voltages and limit the fault currents 
within nominal ranges. It can be seen that the fault currents for the near fault are limited 
within 40kA, which is the nominal short-circuit current, and the voltages are maintained 
higher in both cases. Figures VI.4, VI.5 and Table VI.2 show the simulation results. 



FftLLT r\B=JR 



S 1 



a 

^ 



2DO 

150 

12S 

1GO 

75 

SO - 



- v™ L.JOQJ3 






























\ 


t 








\ 




r 








V 












\ 




J 








nL_ 




f 








^ 






AZ 












\ 














I 






asoo 



o.aeo 



1.000 



1.050 



1.100 



1.1SD 



1.2QO 



(a) 



FAILLT FSBOJR 



2DQ -i 


— u™ inan 


T — 


I 






r- 








1/i= - 
ISO - 
125 - 
100 - 






rV 








-^ 










\ 








J 










\ 








t 






75 - 






\ 








I 










I 








I 






so - 






\ 




















\ 
















25 - 






\ 


















\ 




I f 






— »l ■ t n *m=njt 


ao - 
BO - 

40 - 

ao - 





n . 














/ \ / 


\ A 


p* f 


\ A 










/ \ / 


\ /\ 


\ / 


\ A 












/ \ I 


\ ' \ 


/ 1 / 


\ / \ 


r^ -* — * 


■<• — ■- 


,*— ^ ^ — s 


-2D - 
-40 ~ 






\I 


\ / \ 


' \ / 


\ ' \ 


r~ 










V 


V \ 


' \f 


V \ 


i 












" l x 


> \f 


v V 


I 






-60 -I 























Q93D O.Q75 1.COO 1.Q2S 1.CSO 1.075 1.100 1.125 1.1SO 1.175 



(b) 



41 



f 









ROJULT IVBVR 






20O - 
175 ■ 


- Vmn; IfWI 


\ 


~f 1 


1SO - 

125 - 

100 - 

75 - 

50 " 




^ 




j 


















1 


1 










\ 1 


J^ 






lOO - 


■railTH fCTNT 














SO - 


























60 - 
40 - 




















































-2D - 






















-40 - 













































0.90O 



D953 



1.000 



IjQBO 



1.1G0 



1.150 



1.2GO 



(c) 



Figure VI.4 Simulation results for the fault near the TCSR: The TCSR is required 
to be operated as fault current limiter and voltage restorer, (a) The bus voltage 
is operating in low level when the series reactor is inserted, (b) The fault current 
is exceeding the nominal value when the series reactor is bypassed, (c) Voltage is 
maintained higher and the fault current is limited within nominal value when 
the control scheme is applied. 



FALLTFWR 



ft 



-95 
19GLO 
18BLO 

ieao 

175.0 
17UO 
16&D 

ieao 

155.0 
150LO 
14S.O 



-ifrrre UQ&D 


















| 












































































































aeo 



II HO 



LOO 



1.10 



1.20 



1.30 



T3b 



(a) 



42 



FALLT RftR 



f 

33 






195.0 

190.0 

18&0 
18Q0 
1750 
170.0 
165.0 

iaao 

155.0 

isao 

145.0 

15.0 
125 



-iao 



- vittk i nan 




\ 


f 










\ 


I 










\ 


1_ 










\ 


r^ 















































































■ wiiTn RF^MT 



10.0 - 




aao 



O.90 



1.CO 



1.1Q 



120 



1.30 



1.40 



(b) 



FALLT FAR 



19SO 
190.0 
185.0 
180.0 
175.0 
1TO.O 
16SO 
163.0 
1550 
15QO 
1450 

150 

12.5 

1QO 

7.5 

5.0 

2.5 

O.O 

-25 

-SO 

-75 

-10.0 



- vvttc i nan 





\ 


/ 










\ 


J 










\ 


f 










v 


r^ 














































































■BMITf!F5 


FMT 






































1 fl JL ft M ft 












- 1-| | i\ |i j| i\ 












ill 1 J I] 


















! -If 1 




U '11 IK j 












U Ir V V V B 


1 













080 



0.90 



1.00 



1.10 



1.2D 



1.30 



1.40 



(C) 



Figure VI.5 Simulation results for the fault far away from the TCSR: The TCSR is 
required to be operated as voltage restorer, (a) The bus voltage is operating in 
low level when the series reactor is inserted, (b) The voltage is maintained higher 
and the fault current is in low level when the series reactor is bypassed, (c) 
Voltage is maintained higher and no control action is required to limit the fault 
current. 



43 



Effects of TCSR on Bulk Power System Voltage Stability 

To assess the benefits of the TCSR from the stability point of view, computer 
simulations have been performed with a bulk power system where the total demand is 
73,000MW. A typical power system shown in Figure VI.6 is used for the voltage stability 
assessment. 



Installing TCSR 




Splitted 345kV Buses 



Figure VI.6 A 345kV transmission network for the voltage stability simulation: 
three substation buses can be reconnected when the TCSR is installed. 



To deal with the possible fault currents and voltage stability problems, the network is 
operated by splitting buses and inter-change flow on some transmission lines is 
constrained. For the voltage stability assessment, a fault is applied far away from the 
TCSR. In this case, it does not need to operate as a fault current limiter, because fault 
currents cannot propagate farther as shown in Table VI. 3. It can be seen that the fault 
currents of other buses far away from 4400 bus are considerably reduced. With the 
benefit of proposed control actions of the TCSR, we can expect that the voltage will be 



44 



maintained higher, and accordingly the voltage stability can be maintained with less 
dynamic reactive reserves. The interchange flows are increased to 300MW and 475MW, 
so the available transfer capability of 175MW is achieved. Fault currents are limited 
within nominal ratings resulting in the reconnection of three split 345kV buses. In 
addition, this reduces the transmission losses by 3MW at normal operating conditions. 
The simulation results are summarized in Tables VI.4, VI.5 and Figure VI.7 shows the P- 
V Curves on a special contingent case. 



Voltage [P.U.] 
l.OS 

1.02 

_ 
0.9S 
0.96 
O.S4 
0.92 
OS 
OSS 
O.S6 




Without TCSR (Contingency-state) 



O 100 200 300 400 500 600 700 300 1200 1600 2000 2+00 2500 



Flow 
~[MW] 



Figure VI.7 P-V curves during normal and contingent conditions: maximum 
incremental transfer is increased from 300MW to 475MW when the TCSR is 
used. 



Table VI.2 Comparison results of the voltage and the fault current 







Voltage(kV) 




Condition 










Prefault 


During the fault 


Postfault 


Without TCSR 


186.38 


148.5 


186.38 


With TCSR 


193.9 


176.2 


193.9 


Without TCSR 


186.38 





186.38 


With TCSR 


193.9 





193.9 



Fault Current(kA) 



FAR 



NEAR 



9.5 

11.2 
37.1 
38.5 



45 



Effects of TCSR on Bulk Power System Angle Stability 

On the other hand, if the fault occurs near the place where the TCSR is installed, 
e.g., a generation site, it should act both as a fault current limiter and a voltage restorer. 
Fault current limitation and voltage restoration are controlled by a process of changing 
the impedance of the TCSR, and angle stability is highly related to the impedance behind 
the machine. Therefore, the power system angle stability can be enhanced by changing 
the impedance of the TCSR. Based on the concept of Equal Area Criterion [17], power 
system synchronism can be maintained under the condition where the accelerating power 
is smaller than the decelerating power. 

Generator 
output Power 




Double Circuit 
Condition 



Single Circuit 
Condition 



FCL Operation 
Condition 

Faulted 
Condition 
Power Angle 

I.S : Initial State F.S : Final State A.P : Acceleration Power D.P : Deceleration Power 

Figure VI.8 Power angle curve for Equal Area Criterion: power system 

synchronism can be maintained when the accelerating power is smaller than the 
decelerating power and inserting the series reactor decreases the accelerating 
power as much as the hatched area. 



46 



Considering a Single Machine Infinite Bus (SMIB) system where double circuit 
transmission line is connected in parallel, network conditions can be represented as: (1) 
Prefault (both circuits in service), (2) During a three-phase fault, (3) Postfault (circuit 2 
out of service) and those are illustrated with P-8 plots in Figure VI. 8. When a short- 
circuit fault occurs, the TCSR reduces the accelerating power as much as the hatched area 
by inserting the series reactor at the initial stage of the fault. 




MH=3 



Figure VI.9 Network configuration for the transient stability simulation: a FCL 
using permanently-inserted series reactor is installed on a substation and two 
contingency cases (Fl, F2) are studied to analyze the influences of the FCL on 
the power system angle stability. 



To assess an impact of the TCSR on the bulk power system angle stability, another fault 
is applied near the TCSR as shown in Figure VI.9. A permanently inserted series reactor 
was installed to limit the short-circuit current and a Special Protection Scheme (SPS) 
such as transfer-trip of some loads and generators, etc. has being applied. In this specific 
case, simulation shows that the critical clearing time can be increased more than 50msec. 



47 



Table VI.3 Fault current of the adjacent buses with respect to 4400 bus fault 



Level 


^^^^ Faulted bus 
Adjacent bus^^^^^ 


4400 


4600 


6950 


2400 


4450 


2600 


3250 







55.4 


49.7 


50.5 


34.8 


34.8 


31.0 


47.5 


1 


4600 


34.7 


15.0 












6950 


29.5 




21.0 










2 


2400 

4450 


10.2 
16.0 






24.6 


18.8 






3 


2600 


1.2 










29.8 




3250 


17.3 












30.2 



Table VI.4 Fault current of critical buses(kA) 



Bus number 



Without TCSR 



With TCSR 



Rating 



1400 
1500 
2500 



43.08 
43.94 
51.05 



35.34 
36.67 
48.25 



40 
40 
50 



Table VI.5 Case summary(MW) 






Division 


Transmission loss 


Max. Incremental Transfer 


Without TCSR 
With TCSR 


1070 
1067 


300 

475 



Table VI.6 Critical Clearing Time(msec) 






Fault Location 


Without TCSR 


With TCSR 


Difference 


Fl 

F2 


70 
50 


160 

100 


90 

50 



Furthermore, considering circuit breaker braking time, we can reduce the number of 
generators to be tripped when some generators should be tripped with SPS. Figures VI. 10, 
VI. 1 1 and Table VI.6 show the simulation results using PSS/E. With the control action of 



48 



the TCSR, the output power of the machine and the system voltage can get to a new 
stable operating point. 





r r 


1 1 


1 1 

With TCSR 


1 


r i 


















— 


1 f 
ll 




> 
■ i 




i - H ! !i ii 1 


^rtTi 








^*--s-^ "N 


■ ■ ii 


i 


i ■■ t*i\ • * * ! ■ 








* \ * \ i 


i * 


I * \ 1 1 1 1 '! 


— 






ii • ■ 




■ ' ' 1 ' I \ ■ I 1 l -T 






-■ 


il l ! 

i- i i i : 


• i 


* ■ ! ■■ ■ |i r ' 
! ■'.'!<■ • • 






I 
'- 


i : : : r 


i i 


• •!■■•■• i 
i ■ l i i \ r i 
■ ■ i ■ i ' ■ i 






■ 


t ■ r K 










1 


\ i : ' 

t K 1 •• ! 


i : 

1 i 
■ i 

u 


• ■ s ^ i i ! ■ i J > 
■ ■ ■• ■■ V ! 

pi i; i! r 

1 !i_ 






i- 


i 

.- 


u 




1 ■ 


1 1 


■ ■ 


1 


■ ■ 






I ° 



is 



10 [SEC] 



(a) 



With TCSR 
Without TCSR 










■t-t- 









¥ ^ F 



V 



-5 



* 



10 [SEC] 



(b) 



Figure VI.10 Simulation results on Fl fault: the power system can maintain 

synchronism with the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage 
[P.U.]. 



49 



WithTCSR 

Without TCSR 




h 



;■ - 






10 [SEC] 



(a) 



With TCSR 
Without TCSR 




■ i J 



' * ' I'm 

I ■ ■ Li ■# =1 



3 

i 

-. 



■- 

h 13 



10 [SEC] 



(b) 



Figure VI. 11 Simulation results on F2 fault: the power system can maintain 

synchronism with the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage 
[P.U.]. 



50 



CHAPTER VII 

CONCLUSION 

Various kinds of Fault current limiters (FCLs) are being applied in a distribution 
and transmission network. However, because of the disadvantages on power system 
operations, such as transmission losses and inferior system stability, their usage has been 
limited, which has adversely resulted in more investments on constructing transmission 
lines, replacement of switchgear and degrading the system reliability. However, as the 
transmission network is meshed and more generations are interconnected to the grid, a 
capability to deal with both fault current and power system stability is required. This 
paper has shown that fault currents and stability problems can be managed with the 
TCSR and a PI controller. It has also been shown that the TCSR can maintain the voltage 
higher during the fault situation. For the bulk power system, the proposed approach can 
enhance the system reliability by reducing the number of split buses and increase the 
available transfer capability and critical clearing time. The validity of the proposed 
control scheme has been verified with computer simulation using Matlab, 
PSCAD/EMTDC and PSS/E. The proposed method can be a viable option for the power 
system planners and operators to make countermeasures to cope with fault current and 
stability problems. 



51 



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53